Quantum corrections to holographic entanglement entropy

By T. Faulkner, Aitor Lewkowycz, J. Maldacena. 2013

903 citations recorded by the source corpus.

A bstractWe consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by Ryu-Takayanagi. Here we describe the one loop correction to this formula. The minimal surface divides the bulk into two regions. The bulk loop correction is essentially given by the bulk entanglement entropy between these two bulk regions. We perform some simple checks of this proposal.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/483aa2beb9d6f35006989dad108d748e63daba79

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. D. Harlow
2. D. Stanford
3. S. Raju
4. S. Shenker
5. J. Maldacena
6. R. Myers
7. Ahmed Almheiri
8. Zhenbin Yang

In Nuclear and High Energy Physics

1. D. Harlow
2. S. Raju
3. R. Myers
4. J. Maldacena
5. D. Stanford
6. Thomas Hartman
7. T. Takayanagi
8. V. Hubeny

In Statistical and Nonlinear Physics

1. D. Harlow
2. S. Raju
3. R. Myers
4. D. Stanford
5. J. Maldacena
6. Thomas Hartman
7. S. Shenker
8. V. Hubeny

Citations in the corpus

• Causality & holographic entanglement entropy (2014, background): “Turning next to 1/N , or bulk quantum corrections, while we have less control in general, we can make some observations about the leading 1/N correction which has been proposed to be given by the entanglement of bulk perturbative quantum fields across EA [47].”
• Gravitation from entanglement in holographic CFTs (2013, background): “Thus, the first law should place constraints on the quantum behaviour of the bulk gravitational theory and will likely also involve an understanding of the quantum corrections to the Ryu-Takayanagi formula as discussed recently in [59–61].”
• Space from Hilbert Space: Recovering Geometry from Bulk Entanglement (2016, background): “Because all subsequent higher-partition entanglement information is encoded in the mutual information between all suitably chosen partitions, the approximate geometric information above the chosen scale of partitioning can be characterized by the graph representation.”
• Holographic duality from random tensor networks (2016, background): “This confirms that the holographic mapping defined by a random tensor network maps a weakly-interacting bulk state to a boundary state with a scaling dimension gap, consistent with the expectations of AdS/CFT.”
• Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects (2013, result): “8,39]. Similarly, quantum corrections to the hyperbolic black brane entropy will correspond to 1=Ncorrections to SEE [40]. A precise proposal for the form of the leading 1=Ncorrection appears in ref. [41]. Our results may help to compute such higher-curvature and/or quantum corrections in the duals ”
• Loops in AdS from conformal field theory (2016, background): “For instance, a large N CFT whose entanglement entropy obeys the Ryu-Takayanagi formula [23], but not the Faulkner-LewkowyczMaldacena correction term [24], cannot be dual to Einstein gravity coupled to matter.”
• The Ryu–Takayanagi Formula from Quantum Error Correction (2016, methodology): “So we must instead rely on the derivations of [21,23] to establish the RT formula, after which we may use Theorem 1.”
• Bulk locality from modular flow (2017, background): “A natural mapping of subregions r(R) is suggested by the holographic entanglement entropy formula [7, 8, 9]:”
• Holographic entanglement entropy for general higher derivative gravity (2013, background): “ome back to later. 2After all, string theory predicts such 0-corrections. Note that another natural question involves higher-loop corrections which are not subjects of this paper but were analyzed in [8,9]. { 2 { holographic entanglement entropy gives the correct universal terms for Gauss-Bonnet gra”
• Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime (2014, background): “Our ideal candidate for a formula for holographic entanglement entropy in a nonclassical bulk should therefore (1) be sensitive to quantum effects at any order in ~, (2) reproduce the classical HRT formula at O(~−1), and (3) reproduce the result of FLM at O(~0).”
• Deriving covariant holographic entanglement (2016, background): “Following the arguments of [41], one can say that the quantum corrections at first subleading order O ( c−1 eff ) , can be viewed as the entanglement entropy of region RA in the bulk (suitably regulated).”
• Gravitational dynamics from entanglement “thermodynamics” (2013, background): “According to [18], 1/N corrections to the CFT entanglement entropy correspond to bulk quantum corrections including the entropy of entanglement of bulk quantum fields across the extremal surface.”
• Proof of the Quantum Null Energy Condition (2015, background): “A generalized entropy can be ascribed not only to horizon slices, but to any surface that splits a Cauchy surface [28–32].”
• Low-dimensional de Sitter quantum gravity (2019, background): “[87–97]), it should be fruitful to import these ideas to study the emergence of time in de Sitter.”
• Bit Threads and Holographic Entanglement (2016, background): “Perhaps more interesting, however, is the fact that entanglement of the bulk quantum fields contributes to the boundary EE [33].”